CN104303017B - Deconvolution method for emissions measurement - Google Patents
Deconvolution method for emissions measurement Download PDFInfo
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- CN104303017B CN104303017B CN201280020073.6A CN201280020073A CN104303017B CN 104303017 B CN104303017 B CN 104303017B CN 201280020073 A CN201280020073 A CN 201280020073A CN 104303017 B CN104303017 B CN 104303017B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
- G01N33/0004—Gaseous mixtures, e.g. polluted air
- G01N33/0006—Calibrating gas analysers
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D18/00—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00
- G01D18/008—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00 with calibration coefficients stored in memory
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D3/00—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
- G01D3/02—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation
- G01D3/022—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation having an ideal characteristic, map or correction data stored in a digital memory
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- General Health & Medical Sciences (AREA)
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- Sampling And Sample Adjustment (AREA)
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Abstract
A method of correcting a response of an instrument includes determining an inverse convolution function, the inverse convolution function being in the time domain. A response of an instrument to an exhaust sample is recorded as a function of time. The recorded response is then convolved with the inverse convolution function, the result being a convolution corrected instrument response.
Description
Related application
This application claims the priority of the U.S. Provisional Application No. 61/468,112 of the submission of on March 28th, 2011.
Background technology
Emissions analysis instrument or measuring instrument are used to measure time dependent some gases in waste gas or aerosol sample
Composition, or be configured to measure the particulate matter in such as exhaust sample, such as flue dust.However, due to measured value and the instrument
Convolution between some other signals of the expression transmission function of device or transient response, the response of instrument may not corrected.Uncoiling
Product is the process for inverting or correcting convolution effect.
In a kind of known method, the response of online record instrument in the time domain.In subsequent treatment as follows
The deconvolution of the signal that off-line execution is recorded：（1）Recorded data is decomposed into by time domain by Fourier transformation,（2）Make
Remove the effect of convolution with model, and and then（3）The convolution correction letter for being returned as time domain is formed by inverse-Fourier transform
Number.
The content of the invention
Disclose a kind of method for the response that rectifies an instrument.The method includes determining warp Product function, the deconvolution letter
Numerical digit is in time domain.The method further includes grapher to the time dependent response of exhaust sample, and to being recorded
Response and warp Product function carry out convolution, be as a result that convolution rectifies an instrument response.
Further disclose a kind of method for determining warp Product function.The method includes determining idealization convolution letter
Number, the idealization convolution function is located in time domain.From spatial transform it is frequency domain by the idealization convolution function, and by regularization
Filter function is divided by transformed idealization convolution function.The result of the division is the warp Product function in frequency domain.Then should
Warp Product function is time domain from frequency domain transform.
According to drawings below and describe these and other feature for being better understood on the disclosure in detail.
Description of the drawings
Accompanying drawing can be briefly described below：
Fig. 1 diagrams include the example system of the measuring instrument for being configured to respond waste gas.
The illustrative methods of the response of Fig. 2 diagram correcting measuring apparatus devices.
Fig. 3 represents the detailed step of first step in Fig. 2.
Fig. 4 represents the detailed step of second step in Fig. 2.
Fig. 5 represents the detailed step of third step in Fig. 2.
Specific embodiment
Fig. 1 diagrams include the example system 10 of electromotor 12 and the flue gas leading 14 positioned at the downstream of electromotor 12.As showing
Example, electromotor 12 can be the independent electromotor in the electromotor or laboratory of vehicle.Electromotor 12 can also be including diesel oil
Any types electromotor of machine.
The waste gas 20 produced from electromotor 12 flows to the downstream of electromotor 12, is drawn at 22a, and the sample of waste gas 20
This 24A is drawn towards sample line 22b.A part of 24b of sample 24a is drawn towards measuring instrument 26, and another part 24c be drawn towards with
The parallel Rose Box 28 of measuring instrument 26.But, Rose Box 28 need not necessarily exist.
In this example, measuring instrument 26 is Russ sensor, the micro- smoke sensors of such as AVL483（MSS）.Carry out measurement
The response of instrument 26（Or signal）Represent time dependent soot concentration in a part of 24b of sample 24a.
Can communicate with measuring instrument 26 for the controller 30 of any known type computer, to record the sound of measuring instrument 26
Should.As understood by those skilled in the art, controller 30 may include processor（Or CPU）, screen, hardware driver, mouse,
Keyboard etc..Controller 30 is additionally configured to perform each calculating in following each steps, and can be configured to and system 10
In the communication of other various parts.
Reference gas source 32 optionally connects via adjustable valve 34 with sample line 22b.In one example, controller
30 are configured to regulating valve 34, and but, valve 34 can be manually adjustable.In this example, reference gas are with known
The gas of soot concentration.However, as according to as will be appreciated herein below, reference gas source 32 may include appropriate reference gas.
Though it is shown that Russ sensor, it will be apparent that the disclosure extends to other types of measuring instrument.For example, originally
Open extending to is configured to measure one or more gas componant in exhaust sample（Such as CO2、CO、NO、NO2、NOX、
CH4、HC、O2、NH3、N2O）Amount（Such as, concentration）Gas analyser.Disclosed method can be further used for from any
The data that can determine convolution graph of measuring instrument（Such as measured value of temperature, pressure, flow, speed and torque）Solved
Convolution.Similarly, system 10 is also nonrestrictive, and the disclosure extends to other system and devices, including on road or
The system and device arranged used in laboratory.
Fig. 2 shows the high level overview of each step in an example of disclosed method.As illustrated, in 100,
The response that measuring system 10 changes to step input signal（The specifically response of measuring instrument 26）.Then, respectively in 200 Hes
Idealization convolution function and warp Product function are determined in 300.Before the data during electromotor operates are obtained, can off-line execution
Step 100,200,300.
Then, used in four steps 400 from the result of step 100 to 300, come to during electromotor operates by surveying
The data that measuring appratus are obtained carry out deconvolution.In one example, the data are obtained during exhaust pollution experiment.Optional
Can be to the further precision processing of data after deconvolution in 5th step 500.Step 100 is discussed in detail below to 500.
As those skilled in the art can directly understand, the function in time domain is represented as such as n (t), and frequency
Same Function in domain is represented as N (f).This labelling method is applied in entire chapter application documents.
Fig. 3 shows the detailed step of step 100.In 102 to 106, by positioning to valve 34, by reference gas
Sample（It has the known quantity of measurable exhaust gas constituents）It is connected to measuring instrument, and the non-calibration response x of grapher
(t).As it was previously stated, in measuring instrument 26 is the example of Russ sensor, reference gas have known soot concentration.It is similar
Ground, if measuring instrument is configured to measure HC, can select the reference gas with known HC concentration.
In 108, time T is determinedA、TBAnd TC.As generally described, these times be recorded signal amplitude it is relative
Time point of the known signal in three different percent values.This is represented by declining that measuring instrument and other measuring apparatus cause
Subtract.In this example, to TA、TBAnd TC10%, 50% and 90% is used respectively.
Fig. 4 represents the detailed step of step 200, and its result is to determine idealization convolution function h (t).The function is generally sharp
The approximate of actual convolution function is represented with by Gaussian function with the model that the convolution of impulse response function is formed：
H (t)=g (t) * i (t)
Wherein g (t) is Gaussian function, is defined as：
And wherein i (t) is impulse response function, is defined as：
Ratio τ/σ is determined in step 202., needs ratio τ/σ to carry out normalized convolution function h in step 204n
(t).In one example, ratio τ/σ is determined according to following formula：
In another example, the ratio is determined using look-up table.The input of exemplary look-up table is TA、TBAnd TC。
In step 204, normalized convolution function hn(t).The normalized convolution function is：
hn(t)=gn(t)*in(t)
Wherein gnT () is above-mentioned Gaussian function g (t) of wherein μ=0 and σ=1：
And wherein inT () is wherein τnAbove-mentioned impulse response function i equal to ratio τ for determining in step 202 ./σ
(t)：
Determine that proportionality factor k, proportionality factor k are defined as in step 206：
Wherein TA,nIt is ∫ hnT () reaches the A% of its maximum（It is in this example 10%）Time point, and wherein TC,n
It is ∫ hnT () reaches the C% of its maximum（It is in this example 90%）Time point.
In 208, employable proportion factor k determines parameter σ, μ of idealization convolution function h (t) based on following equation
And τ：
σ=k
μ=kTB, n
τ=k τn
Wherein, TB,nIt is ∫ hnT () reaches the B% of its maximum（It is in this example 50%）Time point.Solving this
After a little parameters, g (t) and the i (t) that can pass through to solve above idealizes convolution function h (t) to determine.
As the alternative step of step 200, idealization convolution function h (t) can be estimated as the response x that do not rectify an instrument
The first derivative of (t).
Fig. 5 generally illustrates each step for determining warp Product function k (t).In 502, by Fourier transformation
Idealization convolution function h (t) is transformed to into frequency domain, it is as follows：
H(f)=F(h(t))
Then, such as 304, regularization filter function R (f) is calculated according to following equation：
Wherein HMAGF () is the amplitude or absolute value of H (f), and wherein α is just adjustable filtering parameter.In an example
In, α is arithmetic number constant value.In another example, α is the function of frequency, and but, constant value is typically enough.Following institute
State, in α is the example of constant, α is adjusted to be suitable to adjust convolution and rectifies an instrument response y (t).
In 306, warp Product function K (f) is calculated by following equation：
K (f)=R (f)/H (f)
Especially, R (f) and H (f) may include plural number, therefore in one example, and above-mentioned division meets removing for two plural numbers
Method rule, and can be by by the value of R (f)（Such as RMAG(f)）Divided by the value of H (f)（Such as HMAG(f)）And from the phase angle of R (f)
（Such as RPHA(f)）In deduct the phase angle of H (f)（Such as HPHA(f)）To perform.
In 308, warp Product function K (f) is converted to into time domain by inversefouriertransform to determine initial deconvolution letter
Number kinit(t)：
kinit(t)=F-1(K(f))
Regularization filter function R (f) depends on just adjustable parameter, and α can be constant value and need not rely upon frequency
Rate.Adjustable parameter generally represents signal to noise ratio.
Once it is determined that kinit(t), in the step 310, to record in step 100 do not rectify an instrument response x (t) with
kinit(t) carry out convolution formed convolution rectify an instrument response y (t), it is as follows：
Y (t)=x (t) * kinit(t)
Then, in step 312, relative to from the known reference gas signal of step 100 assessing convolution rectifier
Device response y (t).In one example, it is estimated by carrying out graphics Web publishing to the two signals, but also can be using one
Dimension optimized algorithm being estimated, with the deviation between the signal that minimizes deconvolution response and represent given data square
With.
As represented in step 314 to 318, can further adjust or " regulation " just adjustable parameter, it is anti-to improve
Convolution function kinitT the accuracy of (), response y (t) is rectified an instrument relative to the reference gas from step 100 so as to improve convolution
The accuracy of body signal.
Regulation depends on change kinitParameter that t constant that () is relied on is just adjustable.Y (t) is estimated in a step 314
Dynamic response（Or slope）, and the overshoot and undershoot of y (t) are illustrated in step 316（Such as amplitude）.As an example, α meetings are increased
Reduce the slope of y (t)（Such as, the worse recovery of dynamic response）, but also reduce overshoot and undershoot.Once draw desired α
（Such as, it is determined that for the α values of the acceptable compromise between the error that represents slope error and caused by overshoot/undershoot）, 320
It is middle to preserve corresponding warp Product function for k (t), so as to used in later-mentioned step 400.
In step 400, do not rectified an instrument using the k (t) preserved in 320 and responded the deconvolution of m (t).
In step 400, system 10 is set to for example as shown in figure 1, so as to control valve 34 so that from the sample of electromotor 12
24a is directly drawn towards instrument 26.
In order to formed convolution rectify an instrument response y (t), to do not rectify an instrument response m (t) with k (t) carry out convolution：
Y (t)=m (t) * k (t)
In one example, controller 30 carries out the convolution of m (t) and k (t) by following Riemann integral：
Wherein, yiIt is that convolution rectifies an instrument i-th value of response vector, mi-(j-1)Be measurement do not rectify an instrument response to
I-th-(j-1) individual value of amount, k ' is overturn in time domain（flipped）Warp Product function（As used in this article, " upset " be
The order of each value in sensing amount is inverted）, n is the quantity of the value in deconvolution functional vector, and j is deconvolution functional vector
Running index, and i is the running index of response vector of not rectifying an instrument.
Due to the multiplication used in 400 and addition intactly calculate in the time domain convolution rectify an instrument response y (t), because
Compared with other methods that other needs are converted between time domain and frequency domain, the calculating in step 400 can be by quick effective for this
Complete.Therefore, using the method for the disclosure without the need for post processing, and convolution school can be online determined during generator operation
Positive instrument response y (t).
In optional step 500, further precision processing convolution can rectify an instrument response y (t) to eliminate in step change
The deviation being likely to occur.In one example, can solve p (t) to calculate the further precision processing, quilt by using following equation
Referred to as derivative correction instrument response p (t)：
Wherein β is constant, and k (t) is the warp Product function in 320, and y (t) is the convolution school obtained from 400
Positive instrument response.In one example, by the use of y (t) as initial valuation iterative p (t) of p (t).Additionally, the 5th step
It is optional, the 5th step can not be included.
Although different examples have particular elements in diagram, it is concrete that various embodiments of the present invention are not limited to those
Combination.Some parts in one example or feature can be used in combination with the feature or part of another example.
It will be recognized by one of ordinary skill in the art that above-described embodiment is exemplary and not restrictive.That is, to this
Disclosed modification should be within the scope of the claims.Therefore, appended claim should be studied, with determine its real scope and
Content.
Claims (20)
1. a kind of method for the response that rectifies an instrument, including：
Determine warp Product function, the warp Product function is located in time domain；
Grapher is to the time dependent response of exhaust sample；And
Response and the warp Product function to being recorded carries out convolution, is as a result that convolution rectifies an instrument response.
2. the method for claim 1, wherein determining that step includes determining idealization convolution function, the idealization convolution
Function is located in time domain.
3. method as claimed in claim 2, wherein the idealization convolution function is the instrument to benchmark exhaust sample
The first derivative of response.
4. method as claimed in claim 2, wherein the idealization convolution function is by Gaussian function and impulse response letter
Number carries out convolution to calculate.
5. method as claimed in claim 4, wherein the Gaussian function and impulse response function are based on proportionality factor, the ratio
Example factor determines according to normalized convolution function and the instrument to the response of benchmark exhaust sample.
6. method as claimed in claim 5, wherein the normalized convolution function is by standardization Gaussian function and standard
Changing impulse response function carries out convolution to calculate.
7. method as claimed in claim 6, wherein the impulse response function based on the instrument to benchmark exhaust sample
Response value.
8. method as claimed in claim 2, wherein determining that step includes becoming the idealization convolution function from the time domain
It is changed to frequency domain.
9. method as claimed in claim 8, wherein determining that step is included regularization filter function divided by transformed ideal
Change convolution function, be as a result the warp Product function in the frequency domain.
10. method as claimed in claim 9, wherein determining that step includes being from the frequency domain transform by the warp Product function
The time domain.
11. methods as claimed in claim 9, wherein the regularization filter function is based on transformed idealization convolution function
Just adjustable filtering parameter.
12. methods as claimed in claim 11, wherein the just adjustable filtering parameter is the constant for being independent of frequency.
13. methods as claimed in claim 12, wherein determine that step includes the adjustment just adjustable filtering parameter, to adjust
State overshoot, undershoot and the dynamic response of warp Product function.
14. the method for claim 1, wherein the instrument is configured as measuring the gas componant of the exhaust sample
The gas analyser of time dependent concentration.
15. the method for claim 1, further include to calculate derivative correction instrument response, to eliminate in step conversion
The noise that Shi Suoshu convolution rectifies an instrument in response.
16. the method for claim 1, wherein solving p (t) by using following equation to calculate derivative correction instrument sound
Should：
Wherein p (t) is the derivative correction instrument response, and β is constant, and k (t) is the warp Product function, and y (t) is institute
State convolution to rectify an instrument response.
A kind of 17. methods for determining warp Product function, including：
It is determined that idealization convolution function, the idealization convolution function is in time domain；
By it is described idealization convolution function from the spatial transform be frequency domain；
As a result it is the deconvolution letter in the frequency domain by regularization filter function divided by transformed idealization convolution function
Number；And
By the warp Product function from the frequency domain transform be the time domain.
18. methods as claimed in claim 17, wherein the idealization convolution function is by Gaussian function and impulse response
Function carries out convolution to calculate.
19. methods as claimed in claim 17, wherein the regularization filter function is based on transformed idealization convolution letter
Number and just adjustable filtering parameter, and wherein described just adjustable filtering parameter is the constant for being independent of frequency.
20. methods as claimed in claim 19, further include the adjustment just adjustable filtering parameter, to adjust the warp
The overshoot of Product function, undershoot and dynamic response.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US201161468112P | 2011-03-28 | 2011-03-28 | |
| US61/468,112 | 2011-03-28 | ||
| PCT/US2012/029020 WO2012134815A2 (en) | 2011-03-28 | 2012-03-14 | Deconvolution method for emissions measurement |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104303017A CN104303017A (en) | 2015-01-21 |
| CN104303017B true CN104303017B (en) | 2017-05-17 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201280020073.6A Expired - Fee Related CN104303017B (en) | 2011-03-28 | 2012-03-14 | Deconvolution method for emissions measurement |
Country Status (6)
| Country | Link |
|---|---|
| US (2) | US20140019077A1 (en) |
| EP (2) | EP3101573B1 (en) |
| JP (1) | JP5932018B2 (en) |
| CN (1) | CN104303017B (en) |
| CA (1) | CA2831593A1 (en) |
| WO (1) | WO2012134815A2 (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3101573B1 (en) | 2011-03-28 | 2018-08-29 | AVL Test Systems, Inc. | Deconvolution method for emissions measurement |
| JP6827955B2 (en) | 2015-01-09 | 2021-02-10 | エーブイエル・テスト・システムズ・インコーポレイテッド | Systems and methods for detecting leaks in exhaust gas sampling equipment |
| US10101257B2 (en) * | 2015-07-06 | 2018-10-16 | Ngk Spark Plug Co., Ltd. | Particulate detection apparatus and particulate detection system |
| DE102016223489A1 (en) * | 2016-11-25 | 2018-05-30 | Robert Bosch Gmbh | Method and device for filtering a sensor signal of a sensor |
| EP3396398B1 (en) * | 2017-04-27 | 2020-07-08 | Rohde & Schwarz GmbH & Co. KG | Signal correction method, system for correcting a measured signal, as well as oscilloscope |
| CN110657864B (en) * | 2019-10-08 | 2020-12-18 | 三门核电有限公司 | Sensor response time measuring method |
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Also Published As
| Publication number | Publication date |
|---|---|
| EP2691901A2 (en) | 2014-02-05 |
| EP2691901B1 (en) | 2016-08-10 |
| EP3101573A1 (en) | 2016-12-07 |
| CN104303017A (en) | 2015-01-21 |
| EP3101573B1 (en) | 2018-08-29 |
| JP5932018B2 (en) | 2016-06-08 |
| US10520480B2 (en) | 2019-12-31 |
| WO2012134815A3 (en) | 2014-04-10 |
| US20140019077A1 (en) | 2014-01-16 |
| JP2014516404A (en) | 2014-07-10 |
| WO2012134815A2 (en) | 2012-10-04 |
| US20180321205A1 (en) | 2018-11-08 |
| EP2691901A4 (en) | 2015-03-25 |
| CA2831593A1 (en) | 2012-10-04 |
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